Nuts and Volts - September/October 2018

integrator output Vout.

In mode 3, we measure the motor voltage as a function of motor current when the motor is running at constant speed. Since there is no other load, all the motor current is used to overcome friction.

In Figure 7, we can see that the current required to overcome friction varies only from about 9 to 11 mA over the range from 0 to 7V So, in a spin-up from 0 to 7V, we can compensate for friction by subtracting 10.0 mA from the measured motor current.

In mode 4, we set the integration stop point to occur when the rotation rate ƒ is at a precise value. With

7V applied to the motor, adjust VR11 slowly CW until comparator U3 trips off. This sets the spin-up stop point at a known frequency ƒs, measured as described previously. Mode 5 is the main measurement mode — what we’ve been getting ready for. Press the reset button to zero the integrator and the start button to start the spin-up and the VT integration. When the rotation rate ƒ reaches the set point ƒs, latch U3 will turn the motor and the integration off. The DVM will read the 0.1VT product — the last data point needed to calculate M. Table 1 is a spreadsheet showing experimental data and the resulting mass calculation for a range of drive currents I and cut-off frequencies ƒs — all of which should produce the same result. The scatter of the results in Table 1 is a measure of the uncertainty of the mass determination. The average of the five measurements shown is 0.213 Kg. I would expect it to be slightly high because I havn’t accounted for the mass of the rotating parts in the motor which add about 1% to the total moment of inertia. My kitchen scale gives the mass of the rotating cylinder as 0.210 Kg. This little science project tries to give an inkling of the complexity of metrology research. It touches a multitude of areas in physics, electrical engineering, and metrology including energy, power, and moment of inertia calculations, op-amp circuit design, DC motors, error correction, and uncertainty analysis — a perfect combination for a physics or EE lab experiment.

The idea of a fundamental measurement of mass using a motor and a spinning flywheel was chosen because it’s doable with modest hardware and effort. I’m sure that NV readers will see a multitude of refinements and improvements — that is the stuff of metrology.

Refinement of the much more complex watt balance is a process that continues in multiple national standard laboratories around the world and is homing in on a mass uncertainty of three parts in 100,000,000 — roughly the weight of a fly’s wing relative to the kilogram. When that happens, the metric system will finally be defined in terms of the speed of light, the charge on an electron, the Planck constant, and the Cesium frequency. NV

Table 1. Experimental Results.

Mass Experiment Parts List

4 TL071IP U3,U4,U5 Operational Amplifier

1 AD620ANZ U2 Instrumentation Amplifier 1 LM7171BIN U1 Op-Amp 100 mA

2 AGN20012 K12,K40 12V DPDT Relay

1 LT1460GCZ-10#PBF U6 10.00V Reference

1 LS7210 U7 comes with PCB Programmable Timer 3 LEDs 11, 12, 40 Red LED

1 H21A1 OC1 Slotted Optical Switch 2 2N3904 Q15, Q40 NPN Transistor

4 EVQ-11A04M B1,B2,B3,B4 Tactile Switch

3 1N914 D12,D30,D40 Diode

1 MFR-25FBF52-49.9 R3 Resistor 49. 9 ohms 1% 2 MFR-25FBF52-1k R12,R64 Resistor 1K

1 MFR-25FBF52-4.7k R61 Resistor 4.7K 4MFR-25FBF52-15k R1,R11,R13,R14 Resistor15K

3 MFR-25FBF52-10k R2,R41,R42 Resistor 10K 1% 5 MFR-25FBF52-47k R15,R40,R50,R51,R62 Resistor 47K 1% 2 MFR-25FBF52-100k R30,R31 Resistor 100K 1% 1 Digi 496-2316ND C40 Capacitor 0.01 µF 11 Digi 478-3192ND Bypass at op-amps Capacitor 0.1 µF 3 Digi 399-4390ND C1,C12,C64 Capacitor 1 µF

3 Digi 493-1548ND C31,C40,C50 Capacitor 100 µF 1 Jameco 2217781 M1 DC Motor

1 McMaster Carr 7786T12 Flywheel Flywheel, Steel

1 PCB A limited supply is available in the NV webstore and comes with the LS7210* (U7). Gerber files are also available in the downloads. Cylinder Diameter(D) m 0.0351 0.0351 0.0351 0.0351 0.0351 0.0351 AppliedCurrent A 0.0209 0.026 0.0317 0.0317 0.0317 0.0399